4.4 Results
4.4.3 Flow Structures and Their Effects on Flow Field
The predictions of the turbulence shear-stress profiles at two different planes (z/D = 0 and 5) and at different downstream locations are shown in Figs. 4.51 and 4.52 for the velocity ratio R = 9. The trend of the profiles is similar to the case with R = 6, but the value of the shear stress is higher compared to the case with R = 6. Moreover the shear stress predictions in the three regions of wall-jet, wake-like and jet-shear layer are also observed more prominent in this case.
Fig. 4.53: Variation of turbulence shear stress in spanwise direction at different downstream locations for R = 9, y/D = 5.
The value of shear stress v′w′is higher at the jet exit region x/D = 0 near both the edges of the jet compared to the case with R = 6. At the downstream positions the value of the stresses are the similar to the case with R = 6.
obstacle blocks it. However, due to the effect of the jet entrainment and the motion of the jet, the flow field of a jet in crossflow is not exactly the same as that over a rigid obstacle. It is to be noted that, the jet-shear-layer vortices form and dominate the initial portion of the jet and which are a result of the Kelvin-Helmholtz instability (Fric and Roshko, 1994). Since the present study deals with the steady mean flow field, these vortices are not captured in the present investigation. A wake-like region with a complex flow pattern is formed in the lee side of the jet. Very close to the bottom wall, a reverse flow region is formed and the crossflow fluid has been observed to enter this region. After entering, the crossflow travels upstream and observed to be lifted upward by the jet fluid and to be carried downstream together with it. Unlike the flow field in the 2D case, the flow does not recirculate in the present highly 3D case. Here the reverse flow is restricted to a region which is close to the bottom wall.
Fig. 4.54: Mean velocity vector plots superimposed with streamline at different spanwise locations, z/D = 0 and 3 for R = 6 in x-y plane.
Fig. 4.55: Mean velocity vector plots superimposed with streamline at different spanwise locations, z/D = 5 and 6 for R = 6 in x-y plane.
The vertical penetration of the jet is more at the central plane (z/D = 0) than at the other three planes due to the lateral spread of the jet near the side edge of the jet discharge slot. It is also observed that the structures and extent of the reverse flow regions downstream of the jet are different at the three spanwsise planes, thereby demonstrating the three-dimensionality of the flow
Figs. 4.56 and 4.57 show the predicted non-dimensional mean velocity vectors superimposed with streamlines at four different x-y planes in the spanwise direction for the velocity ratio R = 9. In this case the jet trajectory is different from that in the case with R = 6. The undisturbed length of the jet is more in this case and the jet penetration into the crossflow is more compared to the case with R = 6. An interesting effect of the velocity ratio on the flow field is observed in the size of the reverse flow region. For the velocity ratio R = 9, the length of the reverse flow zone is decreased by as much as three slot widths or over 20% compared to that for the velocity ratio R
= 6. The length of the reversed flow region is a function of the pressure field induced by the jet on the wall. At high velocity ratio, the jet lifts from the wall rapidly, so the fluid is rapidly drawn into the jet from the crossflow boundary layer. Therefore the effect of the jet upon the crossflow boundary layer fluid does not persist as far downstream as in the case of a low velocity ratio owing to the proximity of the jet to the wall. At a low velocity ratio the jet remains comparatively close to the wall for a large distance downstream and therefore affects the crossflow boundary layer fluid over a large distance.
Fig. 4.56: Mean velocity vector plots superimposed with streamline at different spanwise locations, z/D = 0 and 3 for R = 9 in x-y plane.
In this case also the flow structures at other spanwise planes (z/D = 3, 5, 6 are different than the flow structure at the jet centre plane (z/D = 0). The jet penetration at the spanwise planes z/D = 5 and 6 (Fig. 4.57) is more compared to the penetration at the corresponding planes in case of R = 6 (Fig. 4.55). The jet is relatively strong and therefore its spread is more in the spanwise direction compared to the case with R
= 6. Therefore the existence of the jet is felt more in the spanwise planes compared to the case with R = 6.
Fig. 4.57: Mean velocity vector plots superimposed with streamline at different spanwise locations, z/D = 5 and 6 for R = 9 in x-y plane.
Figs. 4.58 and 4.59 show the mean velocity field at different y-z planes at various downstream locations (x/D = -0.5, 0, 0.5, 2, 5, 10, 15 and 20) for the velocity ratio R = 6. The first plane is located 0.5D upstream of the centre of the jet slot and therefore it is the plane at the leading edge of the jet slot. The crossflow boundary layer fluid not only starts to react to the upcoming jet but also moves away from the bottom wall.
The jet pushes the crossflow in the lateral direction at the edge of the discharge slot since the strength of the jet is more than that of the crossflow. At the centre of the jet slot (x/D = 0), a strong vertical component of the jet velocity is observed. The high velocity jet-shears the relatively slow moving crossflow boundary layer and an inception of two vortical structures is observed at both sides of the jet slot. According to Yuan et al. (1999) these two vortices are formed inside the jet slot itself and they are discharged along with the jet flow.
The roll-up of the crossflow fluid into the cross-streamwise vortices at the edges of the jet is seen at the trailing edge of the jet slot (x/D = 0.5) and the vortices formed
due to the shearing of the crossflow boundary layer flow have moved away slightly from the bottom wall. Downstream of the discharge slot (x/D = 2), the two vortices formed at the edge of the jet move further up from the bottom wall. Due to the absence of a shearing action of the jet the two vortices become weaker and their shape starts to distort. Additionally a pocket of vorticity has appeared on each side of the slot centreline with the same sign of rotation as the vorticity on its respective side.
Further downstream of the jet slot (x/D = 5), the vortices produced at the side edge start to weaken and the two vortices formed at each side of the slot centre plane start to enlarge. The continued development of the CRVP which grows larger in size is observed at the planes x/D = 10, 15 and 20, respectively.
The size of the vortex pair at the plane x/D = 10 becomes very large. The pressure drop in the wake-like region induces an inward motion, transporting the fluid from the crossflow towards the jet centre plane. The development of the CRVP appears to be full fledged at x/D = 15, which grow in size and assume the shape of a kidney. Far downstream the kidney shape of the CRVP is observed to be reduced.
Fig. 4.58: Mean velocity vector plots superimposed with streamline at different downstream locations, x/D = -0.5, 0, 0.5 and 2 for R = 6 in y-z plane.
Fig. 4.59: Mean velocity vector plots superimposed with streamline at different downstream locations, x/D = 5, 10, 15 and 20 for R = 6 in y-z plane.
Fig. 4.60: Mean velocity vector plots superimposed with streamline at different downstream locations, x/D = -0.5, 0, 0.5 and 2 for R = 9 in y-z plane.
The mean velocity field at different y-z planes at various x/D locations (x/D = -0.5, 0, 0.5, 2, 5, 10, 15 and 20) for the velocity ratio R = 9 is shown in Figs. 4.60 and 4.61.
The mechanism of formation of the two vortices at the side edges of the jet is similar to the case with R = 6. However their size and the extent of the affected flow field are more in this case compared to the case with R = 6. The shearing of the crossflow boundary layer flow at the centre plane of the jet (x/D = 0) is more due to a higher velocity of the jet and the size of the two vortices formed at the side edge of the jet is bigger than that in the case with R = 6. The roll-up of the crossflow fluid into the cross-streamwise vortices at the trailing edge of the jet slot (x/D = 0.5) looks similar to the previous case. The sizes of the two central vortices formed at the downstream
locations (x/D = 2) are bigger in this case. Further downstream (x/D = 5, 10, 15 and 20) the structures of the flow field are quite different from those for R = 6. At all these planes the sizes of the CRVP are elongated. At the plane x/D = 10, the two vortex centres are somewhat far from the central plane (z/D = 0). At farther downstream locations (x/D = 15 and 20) the vortex centres come closer to the central plane and also move up. Also the fluid beneath the two CRVP experiences some changes of patterns and direction of rotation. The direction of this rotation is opposite to the rotation of CRVP. At the plane x/D = 20 the bottom part of fluid rotates in the opposite direction and forms other vortices.
Fig. 4.61: Mean velocity vector plots superimposed with streamline at different downstream locations, x/D = 5, 10, 15 and 20 for R = 9 in y-z plane.
Figs. 4.62 and 4.63 show the mean velocity distributions of the jet stream into the crossflow at four different x-z planes parallel to the bottom wall for the velocity ratio R = 6. The first plane (y/D = 1) is located near to the bottom wall. The approaching crossflow boundary layer encounters an adverse pressure gradient ahead of the vertical jet. Since the jet is not a bluff body the separation of the crossflow does not occur but it embraces the side edges of the jet thus forming weak structures of horse shoe vortices. Downstream of the jet slot the jet/crossflow mixture accelerates and converges upon the spanwise centreline (z/D = 0). Immediately downstream of the jet, two vortices roll up. These vortices are both stable spiral nodes and are consistent with the time-averaged ‘wake’ vortices numerically predicted by Rudman (1996), Hale et al. (2000) and Peterson and Plesniak (2004).
Fig. 4.62: Mean velocity vector plots superimposed with streamline at different vertical heights, y/D = 1 and 2 for R = 6 in x-z plane.
It is to be noted that these structures are different from the wake vortex structures reported by Fric and Roshko (1994), which were inherently unsteady. To distinguish them from the wake vortices observed by Fric and Roshko (1994), the steady ‘wake’
vortices are referred by Peterson and Plesniak (2004) as the downstream spiral separation node (DSSN) vortices.
Fig. 4.63: Mean velocity vector plots superimposed with streamline at different vertical height, y/D = 5 and 10 for R = 6 in x-z plane.
Continuing away from the bottom wall to the plane at y/D = 2, the pair of vortices appear to have advected downstream and grown in size. Further away from the bottom wall (y/D = 5), the jet is still almost vertical and expands in the spanwise direction producing a larger wake effect. Therefore the sizes of the two vortices are bigger than those at two other planes. At the plane y/D = 10, the contribution of the crossflow to the in-plane velocity magnitude increases owing to the bending of the jet.
Therefore blocking effect of the jet is lesser and the free stream velocity at this plane is larger in magnitude than that in the first three planes. Therefore the sizes of the two vortices are reduced in the y- direction. As the jet bends and produces no blockage,
the vortices diminish and disappear above the plane y/D = 15 (not shown in Fig.
4.63).
A contour plot of the spanwise component of the mean velocity at different x-z planes is shown in Fig. 4.64. Since the spanwise component plays a leading role in the formation of the CRVP and wake vortices, this plot illustrates the evolution of the flow structures and can give some insight to the formation of those vortices. The first plane corresponds to in-hole contours of the spanwise velocity at a depth of D from the bottom wall
Fig. 4.64: Mean z velocity contour plots at different vertical planes for R = 6.
It is seen that the values of the spanwise velocity at both sides of the jet slot are opposite to each other, thus the tendency of the formation of vortices starts inside the duct itself. The contours of the spanwise velocity at the plane y/D = 0, just before the fluid exits into the crossflow, differ from the previous case. The high-value spanwise components take the position of the side edge and they concentrate there and get ready to exit. The contours of the spanwise velocity at a vertical height y/D = 1 from the bottom wall show different directions of the jet fluid and the crossflow fluid.
Looking in the crossfow direction from the inlet boundary the direction of the spanwise velocity at the right side edge of jet slot is towards the sidewall. These components make the fluid to move in clockwise direction in the right side vortices of DSSN. Just downstream of the jet, the direction of the components are opposite and move towards the centre and they are responsible for the anti-clockwise movement of the right side of wake or DSSN vortices, which can be seen in Figs. 4.62 and 4.63.
.
Fig. 4.65: Mean velocity vector plots superimposed with streamline at different vertical height, y/D = 1 and 2 for R = 9 in x-z plane.
The mean velocity distributions of the jet stream into the crossflow at four different x-z planes parallel to the bottom wall for velocity ratio R = 9 are shown in Figs. 4.65 and 4.66. In the first two planes (y/D = 1 and 2) the DSSN vortices are seemed to be weaker than those in the case with R = 6 and cover a relatively small area
Fig. 4.66: Mean velocity vector plots superimposed with streamline at different vertical height, y/D = 5 and 10 for R = 9 in x-z plane.
One reason for this behaviour may be that for a high velocity ratio, the lift of the crossflow boundary layer flow is large in the jet development region close to the bottom wall (y/D = 1 and 2). The lifted crossflow boundary layer draws the fluid from the DSSN vortices thus having a weak effect in the formation of DSSN. At upward planes (y/D = 5 and 10) the sizes of DSSN and the areas covered by them are more than those in the case with R = 6. In these vertical locations the lifting of the crossflow fluid stops and the jet is comparatively stiffer than that in the case with R = 6 and therefore the wake effect is strong.
Fig. 4.67: Mean z velocity contour plots at different vertical planes for R = 9.
A contour plot of the spanwise component of the mean velocity at different x-z planes for the velocity ratio R = 9 is shown in Fig. 4.67. The spanwise velocity components have similar characteristics as in the case of R = 6, but their values are higher in this case compared to the case with R = 6.